Preheat the oven to 200C/390F.
On a large baking tray, toss the broccoli with a drizzle of olive oil and a good pinch of salt and pepper. Bake in the oven for 15 minutes, or until it begins to lightly char and soften (it will cook more later).
Meanwhile, in a large pan over medium heat add the bacon. Fry until crisp with the fat rendered down, then remove and place to one side, leaving the fat behind. Increase the heat to medium-high and add the chicken to the leftover fat (add a dash more oil if you need to). Season the chicken with 1/4 tsp salt and pepper, then fry until it builds up a golden crust and is just about cooked through (it will cook more later). Remove and place to one side.
Lower the heat back down to medium and melt in the butter. Stir in the flour to create a roux then gradually add in the milk and stock, whisking as you go to prevent lumps from forming. Stir in the mustard and chives, alongside a pinch of nutmeg and pepper (I don't typically add salt due to the bacon and stock). Bring to a gentle bubble, then turn off the heat and stir through the cheese. Once melted, stir through the broccoli, chicken and bacon. Pour into a 25cm x 17cm / 10" x 6.5" baking dish (or similar size) and leave to cool for 10 minutes.
Slice the bagels in half, then slice into chips around 1/4" thick. Neatly layer them over the filling, closing as many gaps as possible. Liberally spray with oil then place in the oven for around 20 minutes, or until the bagel chips and deep golden and crispy with the filling bubbling around the edges. Rest for a couple of minutes then tuck in and enjoy!